Matrix metalloproteinase (MMP) is an endopeptidase that physiologically plays a key role in the tissue remodeling, wherein its protease activity is strictly controlled. In the diseased state, however, the control is disrupted, and the disruption induces excess degradation of extracellular matrix, which in turn is deeply involved in the etiology of many diseases including joint diseases such as osteoarthritis, rheumatoid arthritis and the like, bone diseases such as osteoporosis and the like, periodontal disease, infiltration and metastasis of tumor, corneal ulcer formation and the like (Expert Opinion on Therapeutic Patents, vol. 12, pp. 665-705 (2002)).
At present, MMP is known to include at least 26 different enzymes, which are divided into five groups based on the variation in the primary structure and substrate specificity: collagenase group (MMP-1, 8, 13, 18), gelatinase group (MMP-2, 9), stromelysin group (MMP-3, 10, 11), membrane MMP group (MMP-14, 15, 16, 17), and other group (MMP-7, 12). Of these, MMP-13 belonging to the collagenase group has been reported to almost always express in cartilage and bone tissue, and to show increased production amount in joint disease and the like.
Moreover, since MMP-13 shows a potent collagen degradation activity as compared to other collagenases, it is considered to be deeply involved in the bone and joint diseases.
There are many MMP inhibitors so far reported (e.g., Chemical Reviews, vol. 99, pp. 2735-2776 (1999), Current Medicinal Chemistry, vol. 8, pp. 425-474 (2001)), and a number of reports have also been documented on the compounds showing MMP-13 inhibitory activity. They are largely divided into (i) hydroxamic acid derivatives (e.g., Journal of Medicinal Chemistry, vol. 46, pp. 2361-2375 (2003), Journal of Medicinal Chemistry, vol. 46, pp. 2376-2396 (2003), WO2004/811, WO2003/91247, WO2003/55851), (ii) carboxylic acid derivatives (e.g., Bioorganic & Medicinal Chemistry, vol. 10, pp. 3529-3534 (2002), WO2003/35610) and (iii) thiol derivatives (e.g., Bioorganic & Medicinal Chemistry Letters, vol. 9, pp. 1757-1760 (1999), WO2003/91242) and (iv) others (e.g., Bioorganic & Medicinal Chemistry Letters, vol. 11, pp. 969-972 (2001), WO2003/91252, WO2004/14909), based on the contents thereof.
Meanwhile, as a compound having a heterocyclic amide skeleton, Bulletin of The Chemical Society of Japan, 1990, pp. 72-83 describes a compound represented by the formula

In addition, WO2003/91224 describes a compound represented by
wherein R1 is a hydrogen atom or alkyl; ring Q is a cyclohexylene group or a phenylene group; A1 and A2 are the same or different and each is a single bond or an alkylene group; E is —NHCO— or —CON(R2)— wherein R2 is a hydrogen atom or alkyl; A3 is A31-A32-A33, A31 and A33 are the same or different and each is a single bond, or the same or different 1 or 2 saturated or unsaturated aliphatic hydrocarbon groups at substitutable position(s), which, when one carbon atom has two branched chains, may form a divalent cycloalkyl together with the carbon atom, A32 is a single bond, an oxygen atom, a sulfur atom or —N(R32)— wherein R32 is a hydrogen atom or alkyl; R3 is an optionally substituted acyclic aliphatic hydrocarbon group having 1 to 8 carbon atoms, an optionally substituted mono- to tricyclic cyclic aliphatic hydrocarbon group having 3 to 10 carbon atoms, an optionally substituted mono- or bicyclic aromatic hydrocarbon group having 6 to 12 carbon atoms, or an optionally substituted mono- to tricyclic heterocyclic group; when E is —CON(R2)—, this —N(R2)— and -A3-R3 may form a cyclic amino group; and R4 and R5 are the same or different and each is a hydrogen atom, alkyl, alkoxy, or halogen.